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Chemistry Help Please!

For the reaction: CO(g)+NH3(g)<->HCONH2(g)

The equilibrium constant is: K=0.207 at 400 K.

If a reaction vessel is filled with initial concentrations 2.15M of CO and 2.70M of NH3 and the reactants are allowed to react at 400 K, what will be the concentration of CO at equilibrium?
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1 Answer

This problem can be analyzed using methods similar to those used for buffer solutions.
 
Let x = [CO]     y = [NH3]      z =  [HCONH2]      { these are the concentrations at equilibrium }
 
Since we can view HCONH2 crudely as a CO molecule and and NH3 molecule stuck together, we have
 
x + z  = 2.5
y + z =  2.70
 
These equations can be rearranged to read
z = 2.5 -x
y = .2 +x
 
By the definition of K, we have    K = .207 =  z/(x y)     
Substituting we have
 
.207 = (2.5 -x) /(x (.2 +x))            This equation can be rearranged into the standard
form quadratic equation and solved using the quadratic formula.
 
The solution is x = [CO] = 1.77    (this is easily checked in the previous equation}